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The Scientific World Journal
Volume 2013, Article ID 451091, 4 pages
http://dx.doi.org/10.1155/2013/451091
Research Article

On Flat Objects of Finitely Accessible Categories

Faculty of Mathematics and Computer Science, “Babeş-Bolyai” University, Street Mihail Kogălniceanu 1, 400084 Cluj-Napoca, Romania

Received 6 August 2013; Accepted 8 September 2013

Academic Editors: A. Mimouni and J. Rada

Copyright © 2013 Septimiu Crivei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Auslander and S. O. Smalø, “Preprojective modules over artin algebras,” Journal of Algebra, vol. 66, no. 1, pp. 61–122, 1980. View at Publisher · View at Google Scholar
  2. E. E. Enochs, “Injective and flat covers, envelopes and resolvents,” Israel Journal of Mathematics, vol. 39, no. 3, pp. 189–209, 1981. View at Publisher · View at Google Scholar
  3. L. Bican, R. El Bashir, and E. Enochs, “All modules have flat covers,” The Bulletin of the London Mathematical Society, vol. 33, no. 4, pp. 385–390, 2001. View at Publisher · View at Google Scholar
  4. S. Crivei, M. Prest, and B. Torrecillas, “Covers in finitely accessible categories,” Proceedings of the American Mathematical Society, vol. 138, no. 4, pp. 1213–1221, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  5. W. Rump, “Flat covers in abelian and in non-abelian categories,” Advances in Mathematics, vol. 225, no. 3, pp. 1589–1615, 2010. View at Publisher · View at Google Scholar
  6. M. Prest, “Definable additive categories: purity and model theory,” Memoirs of the American Mathematical Society, vol. 210, no. 987, p. 109, 2011. View at Publisher · View at Google Scholar
  7. W. Crawley-Boevey, “Locally finitely presented additive categories,” Communications in Algebra, vol. 22, no. 5, pp. 1641–1674, 1994. View at Publisher · View at Google Scholar
  8. B. Stenström, “Purity in functor categories,” Journal of Algebra, vol. 8, pp. 352–361, 1968. View at Google Scholar
  9. R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Reading, Mass, USA, 1991.
  10. J. Xu, Flat Covers of Modules, vol. 1634 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1996.
  11. J. Rada and M. Saorín, “Rings characterized by (pre)envelopes and (pre)covers of their modules,” Communications in Algebra, vol. 26, no. 3, pp. 899–912, 1998. View at Publisher · View at Google Scholar
  12. H. Holm and P. Jørgensen, “Covers, precovers, and purity,” Illinois Journal of Mathematics, vol. 52, no. 2, pp. 691–703, 2008. View at Google Scholar
  13. L. Mao, “On strongly flat and -Mittag-Leffler objects in the category ((Rmod)op,Ab),” Mediterranean Journal of Mathematics, vol. 10, no. 2, pp. 655–676, 2013. View at Publisher · View at Google Scholar
  14. B. Mitchell, Theory of Categories, Academic Press, New York, NY, USA, 1965.
  15. N. V. Dung and J. L. García, “Additive categories of locally finite representation type,” Journal of Algebra, vol. 238, no. 1, pp. 200–238, 2001. View at Publisher · View at Google Scholar